Posted
by
kdawsonon Saturday June 13, 2009 @06:54PM
from the that's-odd dept.

radiot88 writes to let us know that he heard a confirmation of the discovery of the 47th known Mersenne Prime on NPR's Science Friday (audio here). The new prime, 2^42,643,801 - 1, is actually smaller than the one discovered previously. It was "found by Odd Magnar Strindmo from Melhus, Norway. This prime is the second largest known prime number, a 'mere' 141,125 digits smaller than the Mersenne prime found last August. Odd is an IT professional whose computers have been working with GIMPS since 1996 testing over 1,400 candidates. This calculation took 29 days on a 3.0 GHz Intel Core2 processor. The prime was independently verified June 12th by Tony Reix of Bull SAS in Grenoble, France..."

They're crunching 13-million-digit numbers with a desktop processor? Do they realize that they can put eight quad-core xeons in a machine and finish the calculation in a single shift instead of waiting a month?

I don't know about you, but the last 13 or so mersenne primes have been found using prime95 as a conduit for a mass distributed effort. I'm not sure where you live, but in most other places people can't just go out and put 8 quad-core xeons in a home machine.

The system used for this is GIMPS, the Great Internet Mersenne Prime Search. The system uses a distributed computing system using unused computing power in personal computers to search for various candidate primes. Computers do one of two things: Either trying to factor candidate Mersenne numbers or running a Lucas-Lehmer test on candidates without any small prime factors (the Lucas-Lehmer test is a special primality test for Mersenne numbers that is very fast). They use modular arithmetic and a variant of the Fast Fourier Transform to handle the multiplications which might otherwise become too difficult. The procedure is naturally a problem that can be made into a parallel processing problem like this since there are so many different candidate numbers to look at.

The summary doesn't mention but it is worth noting that the Lucas-Lehmer test allows one to check the primality of Mersenne numbers (numbers of the form 2^p-1, p prime) much faster than you can test the primality of generic numbers (or almost any other specialized form). Thus, for most of the last hundred years the largest primes known have been Mersenne primes. Currently the largest known prime is a Mersenne prime and the next 4 largest are also Mersenne primes. The GIMPS website - http://mersenne.org/ [mersenne.org] has a lot more details of both the math and software and explains how you can join in to help the project.

It's disappointing that they're using a home-grown management software instead of BOINC [berkeley.edu] like many of the other distributed computing projects. I, for one, would be much more likely to add to the effort if I didn't have to worry about another piece of software and how it shared resources with the Einstein and Rosetta I'm already running.

Do they realize that they can put eight quad-core xeons in a machine and finish the calculation in a single shift instead of waiting a month?

No, they can't. Each iteration of the software requires the results of the previous iteration. It cannot easily be made to run like you want on multiple cores. The best they could do on the processor you describe is run 8 separate copies of the application, each taking one month to run...they could test 8 numbers at once, but they cannot test one number 8 times as fast.

It's less efficient to do this than using each core for one independent number, so it's only used if quick checking of a number is desired (for example, when double-checking a previously found prime number).

"they could test 8 numbers at once, but they cannot test one number 8 times as fast."

Just because most searches use one number per core does not mean testing a single candidate can't be done very efficiently over multiple cores. You only have to think about the process for finding a prime, ie: testing factors, test if the candidate is it divisable by two, three, five, ect. The test for each factor is independent, so you COULD test 8 factors simultaneously, no?

If you were going to test for primality by sieving then you could take a process that is millions of times slower than the primality test used, and speed it up by a factor of 8.

Instead the test being discussed performs a series of squares and modulo reductions. Each operand is dependent on the previous result - the entire computation is one long dependency chain and so cannot be split onto multiple cores in the way that you describe.

Although having said that, it all flips around again if you look inside the

My bad...I misread your processor description...I thought you said 8-core. My answer is still correct though, I just used the wrong number of copies. They can run one copy per core, and the copies cannot exchange information.

As one of the IT guys who maintain the lab that found the 43rd and 44th primes at University of Central Missouri (formerly CMSU), I can tell you its one number per core. Also, these are production machines in computer labs as well as classroom, faculty and staff systems that run the GIMPS software.

We are a public university, its not like we have extra $5k machines just sitting around crunching a number. BTW, the systems that found the 43rd and 44th prime numbers were base model Dell GX280s.

I'm surprised that your 280s could take it. We have a load of those here and the PSUs are all starting to flake out. Even before that, the 280(desktop and SFF models anyway) is not what I'd call well ventilated.

These are all the tower models, which have better air flow. The problem is that systems of that era are subject to the burst capacitors (look for the ones with an X rather than a K or T) and we did have issues with that as well, but we preemptively replaced MBs and PSUs of the of the ones with failing capacitors before our warranty ran out.

As far as running the software, GIMPS is usually pretty good about sharing processor time, and some of the heavier use labs are scheduled to run 9pm-7am.

His brother, Even Magnar Strindmo, is also an IT professional. Even, like his brother Odd, has been testing candidates since 1996. The latest candidate in Even's search was 2^42,643,801-2, which was found to be composite. The very next number, 2^42,643,801-1, was the one his brother found to be prime. "Yeah, it kind of hurts to get so close and not be the one who got it," admits Even, "but I gave it my best game. We agreed back in '96 that we'd split up the work and go even-odd. I guess it was just a matter of luck that he got the first prime. I'm going to keep on trying, though. He's ahead now, 1-0, but if we keep going, I figure at some point I'll pull ahead."

I think he got the joke but decided to enrich people like me, who also got it, but didn't have as high an intrinsic response to the fact that an occurrence of having brothers named Even and Odd isn't out side every day possibility... sort of like a British joke

A few people have both names as well; have a look at the Norwegian White Pages. [gulesider.no]I can't help but think this is some kind of joke from the parents, most Norwegians are reasonably proficient in English.

A Mersenne prime is a Mersenne number that is prime. As of June 2009[ref], only 47 Mersenne primes are known; the largest known prime number (243,112,609 1) is a Mersenne prime, and in modern times, the largest known prime has almost always been a Mersenne prime.[1] Like several previously-discovered Mersenne primes, it was discovered by a distributed computing project on the Internet, known as the Great Internet Mersenne Prime Search (GIMPS). It was the first known prime number with more than 10 million base-10 digits.

For those who can't even remember what a prime is, it's a number that can only be divided (evenly) by 1 and itself. Here's a list of the first primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

The Mersenne primes are the largest known primes.

Prime numbers have applications in electronic security and encryption breaking. I'm not sure what other purpose there is to knowing them, other than knowing them. The Mersenne in particular seem to be merely mathematical curiosities right now.

The historical reasons for caring about Mersenne Prime are twofold: First, Mersenne primes correspond to perfect numbers (numbers that are the sum of their positive less than the number. So for example, 6 has as proper divisors 1,2 and 3 and 1+2+3=6). The ancient Greeks were fascinated by perfect numbers but could not do much to understand them. Euclid showed that if one had a Mersenne prime one can construct an even perfect number. In particular, if 2^n-1 is prime then (2^n-1)*2^(n-1) is perfect. Almost 2000 years later, Euler showed that every even perfect number is of Euclid's form. Thus, investigating Mersenne primes tells us more about perfect numbers. The oldest unsolved problems in math are 1) are there any odd perfect numbers? and 2) are there infinitely many even perfect numbers? Thus, investigating Mersenne primes helps us get closer to solving one of the two oldest unsolved problems in mathematics.

Well, they may be unsolved problems, but again, they look like they have no relevance to anything, no application, other than being unanswered questions. But, like so many things, knowledge is valuable for its own sake, and who knows what revolution may result from what is now just a mathematical curiosity. Stealth-flight technology was originally harvested from a little known paper on radar written by an obscure Russian scientist. Kind of ironic that we were the ones to develop it. What you're really talki

Well, this does actually fit some of the patterns we are beginning to see. For example, there are reasons to expect that for most Mersenne primes 2^p-1 one will have p-1 having many small prime factors (this has to do with Fermat's Little Theorem). We in fact see that again in this case we see that since p-1 factors as 2^3 * 3^3 * 5^2 * 53 * 149. Also, the discoveries are are enough to be noteworthy in the same way that discovery of new elements is noteworthy. We likely won't find out much by itself from th

I would be rather surprised if there weren't an infinite number of primes, just based on the idea of what a prime is and how it's found. It's a sliver of a number, the falls between the divisable boundaries. And the larger the number get, it would seem, the more rare primes should become, this has certainly proven to be true. Hmm, that does seem to imply they would get more rare with time, since the more numbers you have as you increase the count, the more possible factors that exist. But still, that should

We know there are infinitely many primes. This has been known since the ancient Greeks. Proving this is really easy: Assume there are only finitely many primes. Multiple them all together and add 1. This number is greater than 1 and not divisible by any prime number which is absurd. That's a contradiction so our original assumption is wrong and there are infinitely many primes.

What we can't show is that there are infinitely many Mersenne primes. A Mersenne prime is a prime that 1 less than a power of 2.

Actually, you can apparently use larger Mersenne Primes to improve results in totally different but very useful fields, like privacy-related schemes. For example, this paper http://eccc.hpi-web.de/eccc-reports/2006/TR06-127/index.html [hpi-web.de] uses large Mersenne primes to get interesting results on Locally Decodable Codes and Private Information Retrieval Schemes...

That funny E sign means 'element of a set' [techtarget.com] and the set is defined by that funny P sign, which means all primes. This means that Wolfram is saying that 2^42643792 -1 is a member of the set of prime numbers. See also how they know it is a prime. [wolfram.com]

Ah I see what you are saying now, and you are rbarreira is probably right, it has given up. I thought that the input region saying it was a member meant it was true... Oh well, I did think it was pretty impressive that it new so quick!

Ah I see what you are saying now, and you are rbarreira is probably right, it has given up. I thought that the input region saying it was a member meant it was true... Oh well, I did think it was pretty impressive that it new so quick!

According to the The Hitchhiker's Guide to the Galaxy, "Odd Magnar Strindmo" was a fourth generation accounting prefect on the third major planet of the second solar system in the first minor galactic cluster directly to the "left" of the vicinity of Betelgeuse - a star that has recently gone supernova. After achieving a modicum of fame for discovering the 47th known Mersenne Prime, during extended holiday on the, mostly harmless, planet named Earth, Mr Strindmo retired to a life of semi-luxury where he pr